Inverse problem for Lagrangian mechanics

In Lagrangian mechanics, an inverse problem is when you know what motion you want something to follow, but you need to figure out how to make the thing move that way. To solve an inverse problem, you first have to create a Lagrangian, which is a mathematical equation that describes the motion. Then, you can use the Lagrangian to figure out the forces that will cause the object to follow the motion you want.